Mortal matrix problem by Ciro Santilli 37 Updated 2025-07-16
One of the most simple to state undecidable problems.
The reason that it is undecidable is that you can repeat each matrix any number of times, so there isn't a finite number of possibilities to check.
Translation group by Ciro Santilli 37 Updated 2025-07-16
This is a good and simple first example of Lie algebra to look into.
Onion service by Ciro Santilli 37 Updated 2025-07-16
This is a way to host a server that actually hide the IP of the server from the client, just like Tor hides the IP of the client from the server. Amazing tecnology!
This is why it enables hosting illegal things like the Silk Road: law enforcement is not able find where the server is hosted, and take it down or identify the owner.
By looking at this more general point of view, we could ask ourselves what happens to the group if instead of the dot product we took a more general bilinear form, e.g.:
The answers to those questions are given by the Sylvester's law of inertia at Section "All indefinite orthogonal groups of matrices of equal metric signature are isomorphic".
Dr. Strangelove by Ciro Santilli 37 Updated 2025-07-16
Video 1.
Inside the Making of 'Dr. Strangelove' part 2
. Source.
One-time pad by Ciro Santilli 37 Updated 2025-07-16
The only perfect cryptosystem!
The problem is that you need a shared key as large as the message.
Systems like advanced Encryption Standard allow us to encrypt things larger than the key, but the tradeoff is that they could be possibly broken, as don't have any provably secure symmetric-key algorithms as of 2020.
Final Fantasy VI by Ciro Santilli 37 Updated 2025-07-16
OMG, the second half of the game where the world becomes quite open and all backstories are revealed, is one of the best gaming moments ever.
Now, there are two ways to go about this.
The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.
The second is the much celebrated ladder operator method.

There are unlisted articles, also show them or only show them.